# How Does a Diffraction Grating Resolve Different Wavelengths of Sodium Light?

• Eagertolearnphysics
In summary: What is the formula for finding angular dispersion of grating? is it the same as angular width?The angular dispersion of a grating is the angle between the lines of the grating. It is measured in degrees.
Eagertolearnphysics

## Homework Statement

Yellow sodium light, which consists of two wavelengths, λ_1 =589.0 nm and λ_2 = 589.89 nm, falls on a 7500 lines/cm diffraction grating. Determine (a) the maximum order m that will be present for sodium light, (b) the width of grating necessary to resolve the sodium lines, (c) the grating resolving power in this case, (d) the angular width of each sodium line.

## The Attempt at a Solution

(a) I divided λ by Δλ and I found it to be 1000, therefore Nm, where m is the order, will be always larger than λ/ Δλ. therefore i don't get how the problem asks for maximum, however, m = 1 is an answer!
(b) I tried mλ = d sinθ but i don't know what θ to use !
(c) it depends on (b)

Eagertolearnphysics said:
(a) I divided λ by Δλ and I found it to be 1000, therefore Nm, where m is the order, will be always larger than λ/ Δλ. therefore i don't get how the problem asks for maximum, however, m = 1 is an answer!

Perhaps you can explain why you divided λ by Δλ ?

The equation I remember is:
mλ = e * sinθ
where m is the order (1,2,3...)
e is the grating separation
θ is the defraction angle for each m
so
m = e/λ * sinθ

What value of θ gives you maximum m?

CWatters said:
Perhaps you can explain why you divided λ by Δλ ?

The equation I remember is:
mλ = e * sinθ
where m is the order (1,2,3...)
e is the grating separation
θ is the defraction angle for each m
so
m = e/λ * sinθ

What value of θ gives you maximum m?
the problem doesn't include the value of θ

Eagertolearnphysics said:
the problem doesn't include the value of θ
What is the maximum angle you can achieve theoretically?

Biker said:
What is the maximum angle you can achieve theoretically?
π/2

Correct.

So plug that into the equation and calculate m.

CWatters said:
Correct.

So plug that into the equation and calculate m.
But I don't have the grating separation

You have the number of lines in 1cm.
Can't you use that to find it?

Eagertolearnphysics
Yes I can, m = 2.26 but I don't know what to do next !

Last edited:
Biker said:
You have the number of lines in 1cm.
Can't you use that to find it?
what is the formula for finding angular dispersion of grating? is it the same as angular width?

Eagertolearnphysics said:
Yes I can, m = 2.26 but I don't know what to do next !

You remember that m must be an integer ..

## 1. What is a diffraction grating?

A diffraction grating is a scientific tool that is used to separate light into its component wavelengths. It is made up of a large number of closely spaced parallel lines etched onto a surface, which causes light to diffract and produce a spectrum.

## 2. How does a diffraction grating work?

When a beam of light hits a diffraction grating, the light rays are split into different paths as they pass through the grating's slits. This causes the light to spread out and form a spectrum of colors, with shorter wavelengths (such as blue and violet) bending more than longer wavelengths (such as red and orange).

## 3. What are the applications of diffraction gratings?

Diffraction gratings have a wide range of applications in both scientific research and everyday life. They are commonly used in spectroscopy to analyze the composition of materials, in telecommunications to transmit and receive signals, and in optical instruments like telescopes and cameras to improve image quality.

## 4. What factors affect the performance of a diffraction grating?

The performance of a diffraction grating can be affected by several factors, such as the spacing and number of lines on the grating, the angle of incidence of the light, and the wavelength of the light. The material and quality of the grating can also play a role in its performance.

## 5. How do you calculate the angle of diffraction for a diffraction grating?

The angle of diffraction can be calculated using the formula: θ = sin^-1 (mλ/d), where θ is the angle of diffraction, m is the order of the spectrum, λ is the wavelength of light, and d is the distance between the grating's lines. This calculation is based on the principle of diffraction and can help determine the specific wavelength of light being diffracted by the grating.

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